Index filtrations and Morse decompositions for discrete dynamical systems
Annales Polonici Mathematici, Tome 72 (1999) no. 1, pp. 51-70
On a Morse decomposition of an isolated invariant set of a homeomorphism (discrete dynamical system) there are partial orderings defined by the homeomorphism. These are called admissible orderings of the Morse decomposition. We prove the existence of index filtrations for admissible total orderings of a Morse decomposition and introduce the connection matrix in this case.
Keywords:
Conley index, index filtration, Morse decomposition, connection matrix
@article{10_4064_ap_72_1_51_70,
author = {P. Bart{\l}omiejczyk and Z. Dzedzej},
title = {Index filtrations and {Morse} decompositions for discrete dynamical systems},
journal = {Annales Polonici Mathematici},
pages = {51--70},
year = {1999},
volume = {72},
number = {1},
doi = {10.4064/ap-72-1-51-70},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-72-1-51-70/}
}
TY - JOUR AU - P. Bartłomiejczyk AU - Z. Dzedzej TI - Index filtrations and Morse decompositions for discrete dynamical systems JO - Annales Polonici Mathematici PY - 1999 SP - 51 EP - 70 VL - 72 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/ap-72-1-51-70/ DO - 10.4064/ap-72-1-51-70 LA - en ID - 10_4064_ap_72_1_51_70 ER -
%0 Journal Article %A P. Bartłomiejczyk %A Z. Dzedzej %T Index filtrations and Morse decompositions for discrete dynamical systems %J Annales Polonici Mathematici %D 1999 %P 51-70 %V 72 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/ap-72-1-51-70/ %R 10.4064/ap-72-1-51-70 %G en %F 10_4064_ap_72_1_51_70
P. Bartłomiejczyk; Z. Dzedzej. Index filtrations and Morse decompositions for discrete dynamical systems. Annales Polonici Mathematici, Tome 72 (1999) no. 1, pp. 51-70. doi: 10.4064/ap-72-1-51-70
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